Question

what composition transformation rule has triangle lmn, l (1, 1), m (7, 2), and n (5, 7) map onto triangle lmn, l (2, - 1), m (- 4, 0), n (- 2, 5)? note: behind the letters means there are two transformations that have taken place so apply one and then from that one apply the next (1 point) a reflection across the y - axis and a move to the left by 5 and up by 3 a reflection across the y - axis and a move to the right by 1 and down by 2 a reflection across the x - axis and a move to the left by 3 and down by 2 a rotation of 270 degrees clockwise and a move right by 1 and up by 2

Explanation:

Step1: Analyze reflection across y - axis

The rule for reflecting a point $(x,y)$ across the $y$-axis is $(x,y)\to(-x,y)$. For point $L(1,1)$, after reflection across the $y$-axis, it becomes $(- 1,1)$.

Step2: Analyze translation

If we then consider a translation of moving to the right by $3$ units (add $3$ to the $x$-coordinate) and down by $2$ units (subtract $2$ from the $y$-coordinate), $(-1,1)$ becomes $(-1 + 3,1-2)=(2,-1)$ which is $L'$.
For point $M(7,2)$, after reflection across the $y$-axis, it is $(-7,2)$. Then with the translation (right $3$, down $2$), $(-7,2)$ becomes $(-7 + 3,2 - 2)=(-4,0)$ which is $M'$.
For point $N(5,7)$, after reflection across the $y$-axis, it is $(-5,7)$. Then with the translation (right $3$, down $2$), $(-5,7)$ becomes $(-5+3,7 - 2)=(-2,5)$ which is $N'$.

Answer:

a reflection across the y - axis and a move to the right by 3 and down by 2